Physics 492 Lecture 19

Transcription

1 Physics 492 Lecture 19 Main points of last lecture: Relativistic transformations Four vectors Invarients, Proper time Inner products of vectors Momentum Main points of today s lecture: Momentum Example: Photon-electron scattering Nuclear models.

2 Midterm results Exam results 8 7 Midterm 1 grades and average midterm 1 Average = 39 number of students Correlation with homework Score 70 Correlation between homework and exam 60 midterm 1 50 midterm Homework

3 4-velocity and 4-momentum Other 4 vectors value for inner product

4 Use power to calculate energy What is relativistic energy In summary This eq. contains both energy and momentum conservation

5 Example: electron-photon scattering

6 Electron-photon scattering continued

7 Some hints on homework problems 2-5 are can be done with non.-rel. kinematics Williams problem 7.8 has a table. Items on the same row of this table are not necessarily from the same event. For example, the 6.13 MeV gamma ray is not associated with the 1.3 MeV alpha particle. It is associated with the 2.1 MeV alpha particle.

8 Physics 492 Lecture 20 Main points of last lecture: Some notes on relativity Main points of today s lecture: Some notes on relativity Some instructions on the paper. Nuclear models. Shell splitting central potential Spin-orbit term Filling single particle orbits Nuclear Spins and parities

9 Final comments on relativity Comments on Matrix vs. Einstein representation this number is a scalar which does not change under Lorentz transformations Other standard problem: decay

10 Research paper instructions Use Formatting of the Nature paper Read Scientific American or Physics Today and try to adopt the writing style. You can be a little more technical than Scientific American, but don t write much above your level of understanding. Your report will be graded on: Content Scientific understanding (science explanation) Writing: (fluidity and clarity of style and organization) Formatting SCORE = 0 IF HANDED IN LATE! Acknowledge your sources; don t plagiarize Useful research tools: Google Web of Science index

11 Nuclear Models

12 Shell model The Nuclear Shell model is one of the standard techniques for calculating nuclear properties It was originally motivated by the Atomic Shell model Single electron orbits in a combined Coulomb potential from the nuclear charge and the electronic charges. Atomic shells: Lecture Plan for nuclear shell model: Evidence plus qualitative discussion first Model details next

13 Bare Coulomb pot. What are the levels of an atom? Consider hydrogenic orbits Atomic pot.

14 Further consequences of Atomic shell model Atomic separation energies (Energy to remove an electron) What drives these trends

15 Effect of screening on level order? Bare Coulomb pot. M.N. = magic numbers or closed shells Atomic pot. Screening reduces the binding energy of orbits with high angular momentum. Centrifugal potential keeps electrons in state with large orbital angular momentum away from the strong nuclear charge.

16 Consequences of atomic shell model Closed shells denote chemical reactivity Mid shell elements can deform (Hybridize) orbits to maximize chemical bonds

17 Physics 492 Lecture 21 Main points of last lecture: Some notes on relativity Evidence for Nuclear shells. Main points of today s lecture: Some notes on relativity Nuclear models. Shell splitting central potential Spin-orbit term Filling single particle orbits Nuclear Spins and parities

18 Possible existence of nuclear shells Plot S n for odd N nuclei. Pairing has similar effect on all of these points. Plot S p for odd Z nuclei Both plots show decreases in separation energies at closed shells

19 More look more closely at N=126 Examine S n for N even. Δ denotes the change in S n across the shell closure

20 Mass minus liquid drop mass focuses on shell effects M-M LDM (MeV)

21 Possible zeroeth order nuclear potential? Scattering suggests Woods-Saxon (fermi function) form Square well. V=kr 2 pot. Simpler choices? W.S Square well. V=kr 2-50 MeV pot. (H.O. pot.) Nuclear potential.

22 Other tests of shell effect interpretation Nuclear deformation, analog of chemical orbit hybrization: In nuclei, nucleon orbits in open shells deform to maximize overlap with other nucleons Increase nuclear deformation increases the moment of inertia and decreases E I, see the homework.

23 Deformability of nuclear orbits Orbits in closed shell nuclei cannot be deformed. Such nuclei are spherical and have high first excited states Midshell nuclei are easy to deform and have low first excited states Analog of the orbithybridization for mid atomic shell atoms.

24 What s needed to get correct magic numbers? spectroscopic notation: nl J :L=1,2,3..; S,P,D... Spin-orbit interaction is the major missing term

25 Plan of lecture

26 H.O. potential Shift potential down by about 50 MeV to match W.S. Radial equation Features

27 Energy Eigenvalues The result is what you expect for adding the energies of H.O. along x, y and z axes. Note ½ kr 2 = ½ k(x 2 +y 2 +z 2 )